Sephardim and German/Yekke Yidden wear a Tallit from Bar Mitzvah. Having stated the above, it is extremely rare for a Bochur in these communities to cover his head with a Tallis, there are exceptions.
The practice of Eastern European/Litvish & Chassidic bochurim not to wear a Tallis comes from the Rishonim, particularly the Maharil as a practice that is substantiated by a Gemara in Kiddushin which implies that unmarried people can not be on the Madrega to ‘wrap themselves’, whatever exactly that means.
I used to jokingly say that it made logical sense not to wear a Tallis since it would be easily identifiable who is and who is not married, for shidduch purposes.
A mekor for wearing a Tallis by marriage, actually comes from Megillat Ruth in Perek Gimmel, pasuk tet which states that Ruth asked Boaz to spread his garment over her. The Meforshim point out that the incident was the ‘signal’ for these 2 individuals to get married.
The Bnei Yissaschar also point out that a Tallis is equivalent to Ohr Makif which he implies only applies to married men.